G = sym2 F
If tau: F**F \to F**F is the chain map reversing the factors, with appropriate signs, then sym2 F = image(1+tau) = ker(1-tau) = coker(1-tau)
The object sym2 is a method function.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/ChainComplexOperations.m2:326:0.